Trust Region Algorithms Based On The Conic Model

Optimization method is a very strong discipline of applicability, it is an important component of operations research, optimization method can solve a lot of practical problems. Unconstrained optimization is an important branch of optimization. Therefore, studying on such a research is of great significance.For unconstrained optimization problem, how to design a fast and effective algorithm has been much attention, in which trust region algorithm for solving unconstrained optimization problems is a kind of effective method. In recent years, the research on trust region algorithm is more perfect, but for non-monotone trust region algorithm theory research is still not perfect.For unconstrained optimization problem, this paper proposes two non-monotone trust region algorithms based on the conic model, and global convergence is proved under certain conditions.